Deck 20: Waiting-Line Models

Question 1

Study of waiting-line models helps operations managers better understand:

A) service systems such as bank teller stations.
B) maintenance activities that might repair broken machinery.
C) shop-floor control activities.
D) service systems such as amusement park rides.
E) all of these

Answer 1

E

Question 2

In queuing problems, arrival rates are generally described by the Poisson probability distribution.

Answer 2

True

Question 3

A copy center has five machines that serve many customers throughout the day. The waiting line for copy service has a finite population, while the waiting line for copier maintenance has an infinite population

Answer 3

False

Question 4

In queuing problems, the term renege refers to the fact that some customers leave the queue before service is completed.

Question 5

A waiting-line system has three parts: the size of the arrival population, the behavior of arrivals, and the statistical distribution of arrivals.

Question 6

A waiting line or ________ is where items or people are in a line awaiting service; ________ is a body of knowledge about waiting lines.

Question 7

The two characteristics of the waiting line itself are whether its length is limited or unlimited and the discipline of the people or items in it.

Question 8

Waiting-line models are useful to operations in such diverse settings as service systems, maintenance activities, and shop-floor control.

Question 9

If service times follow a negative exponential distribution, the probability of any very long service time is high.

Question 10

In queuing problems, which of the following probability distributions is typically used to describe the time to perform the service?

A) binomial
B) normal
C) Poisson
D) negative exponential
E) lognormal

Question 11

If the service time within a queuing system is constant, the service rate can be easily described by a negative exponential distribution.

Question 12

A waiting-line system with one waiting line and three sequential processing stages is a multiple-server, single-phase system.

Question 13

In the analysis of queuing models, the negative exponential distribution often describes arrival rates, while service times are often described by the Poisson distribution.

Question 14

The common measures of a queuing system's performance include:

A) probability that the service facility will be idle, average queue length, and probability that the waiting time will exceed a specified duration.
B) average time each customer spends in the system, probability that the service system will be idle, and average time each customer spends in the queue.
C) average queue length, maximum time a customer may spend in the queue, and the utilization factor for the system.
D) average time each customer spends in the system, maximum queue length, and probability of a specific number of customers in the system.
E) maximum queue length, maximum time a customer may spend in the queue, and average queue length.

Question 15

Which of the following is NOT a common queuing situation?

A) grocery shoppers being served by checkout clerks
B) commuters slowing or stopping at toll plazas to pay highway tolls
C) machinery waiting to be repaired or maintained
D) parcel delivery truck following its computer-generated route
E) patients in a health clinic waiting to see one of several doctors

Question 16

In queuing problems, which of the following probability distributions is typically used to describe the number of arrivals per unit of time?

A) binomial
B) normal
C) Poisson
D) exponential
E) lognormal

Question 17

LIFS (last-in, first-served) is a common queue discipline, most often seen where people, not objects, form the waiting line.

Question 18

A hospital emergency room typically follows a FIFO queue discipline in the interest of fairness.

Question 19

Balk and renege are elements of queue discipline.

Question 20

A bank office with five tellers, each with a separate line of customers, exhibits the characteristics of a multiphase queuing system.

Question 21

Which of the following represents a customer who reneged due to the waiting line?

A) A husband and wife decide to eat out instead after seeing the movie ticket line.
B) A car drives past the first fast-food restaurant on Hamburger Row because the drive-through was full.
C) A Black Friday shopper skipped one store because the line went around the building.
D) A student ordered pizza online because the phone line was busy.
E) A customer at a gas station went inside to buy a soda, but after waiting in line for a minute left the soda behind and went outside empty-handed.

Question 22

Which of the following is most likely to be served in a last-in, first-served (LIFS) queue discipline?

A) customers checking out at a grocery store
B) the in-basket on a manager's desk
C) patients entering a hospital emergency room
D) patrons waiting to be seated in a casual-dining restaurant
E) customers waiting to see a bank teller

Question 23

Which part of a waiting line has characteristics that involve a statistical distribution?

A) arrivals or inputs
B) the waiting line itself
C) the service facility
D) A and C
E) A, B, and C

Question 24

A McDonald's single-lane drive-through that has one window for making the payment and a second window for receiving the food behaves most like which of the following?

A) single-server, single-phase system
B) single-server, multiphase system
C) multiple-server, single-phase system
D) multiple-server, multiphase system
E) single-server, sequential-phase system

Question 25

The shopper who says to himself, "I've waited too long in this line. I don't really need to buy this product today," and leaves the store is an illustration of which element of arrival behavior?

A) random arrival
B) renege
C) random departure
D) balk
E) frustration

Question 26

Which of the following is most likely to violate a FIFO queue?

A) supermarket with no express lanes
B) car repair garage
C) emergency room
D) fast-food restaurant
E) All of these are equally likely to violate a FIFO queue.

Question 27

A large discount store and supermarket has a hair styling salon on its premises. The salon has several operators. Salon customers can shop in other parts of the store until their name is called for salon service, at which time the customer will be served by the next available stylist. This scenario provides an example of which of the following?

A) multiple-server, limited queue length
B) single-server, multiphase, limited queue length
C) multiple-server, unlimited queue length
D) multiple single-server systems, limited queue length
E) single-server, unlimited queue length

Question 28

The sign at the bank that reads, "Wait here for the first available teller," suggests the use of a ________ waiting line system.

A) dynamic-server, single-phase
B) random-server, single-phase
C) single-server, multiphase
D) multiple-server, single-phase
E) multiple-server, multiphase

Question 29

An airline ticket counter, with several agents for one line of customers, is an example of which of the following?

A) single-server, single-phase system
B) single-server, multiphase system
C) multiple-server, single-phase system
D) multiple-server, multiphase system
E) cross-server, single-phase system

Question 30

A waiting line, or queuing, system has three parts, which are:

A) distribution of arrival times, discipline while waiting, and distribution of service times.
B) arrival rate, service rate, and utilization rate.
C) arrival discipline, queue discipline, and service sequencing.
D) arrivals or inputs, queue discipline or the waiting line itself, and the service facility.
E) sequencing policy, penalty for reneging, and expediting of arrivals.

Question 31

Which of the following is an example of a finite arrival population?

A) copy machines in a copying shop that break down
B) students at a large university registering for classes
C) shoppers arriving at a supermarket
D) cars arriving at a suburban car wash
E) all of these

Question 32

Which of the following is NOT a measure of a queue's performance?

A) average time spent in the queue
B) average queue length
C) probability that the service facility will be idle
D) utilization factor for the system
E) All of these are performance measures.

Question 33

The potential restaurant customer who says to her husband, "The line looks too long; let's eat somewhere else," is an illustration of which element of arrival behavior?

A) first-in, first-out
B) balk
C) renege
D) random departure
E) frustration

Question 34

Which of the following represents an unlimited queue?

A) drive-through lane at a fast-food restaurant
B) small barbershop with only 5 chairs for waiting customers
C) toll booth serving automobiles on an interstate
D) faculty office with limited seating during office hours
E) restaurant with no outside seating and limited capacity due to fire department restrictions

Question 35

A college registrar's office requires you to first visit with one of three advisors and then with one of two financial professionals. This system is best described as which of the following?

A) single-server, single-phase system
B) single-server, multiphase system
C) multiple-server, single-phase system
D) multiple-server, multiphase system
E) multiple-server, cross-phase system

Question 36

A system in which the customer receives service from only one station and then exits the system is which of the following?

A) a single-phase system
B) a single-channel system
C) a multiple channel system
D) a multiphase system
E) a limited-access system

Question 37

Arrivals or inputs to a waiting-line system have characteristics that include:

A) population size.
B) population behavior.
C) population's statistical distribution.
D) A and C
E) A, B, and C

Question 38

The source population is considered to be either ________ in its size.

A) finite or infinite
B) fixed or variable
C) known or unknown
D) random or scheduled
E) small or large

Question 39

Which of the following is a measure of queue performance?

A) utilization factor for the system
B) average queue length
C) probability of a specific number of customers in the system
D) average waiting time in the line
E) all of these

Question 40

A concert hall, employing both ticket takers and ushers to seat patrons, behaves typically as which of the following?

A) multiple-server, single-phase system
B) multiple-server, multiphase system
C) single-server, single-phase system
D) single-server, multiphase system
E) multiple-server, cross-phase system

Question 41

What does it mean to have a patient customer in a waiting line?

Question 42

Suppose that, on average, 4 customers arrive each minute in a Poisson distribution. What is the probability that 2 customers will arrive in a particular minute?

A) 0.500
B) 0.147
C) 0.018
D) 0.073
E) 0.195

Question 43

A(n) ________ queuing system has one waiting line, but several servers; a(n) ________ queuing system is one in which the customer receives services from several stations before exiting the system

Question 44

Suppose that 2 customers arrive on average each minute in a Poisson distribution. Is it more likely that 1 customer or 0 customers will arrive each minute?

Question 45

A(n) ________ occurs when an arrival refuses to enter a waiting line; a(n) ________ occurs when an arrival joins a waiting line, then leaves it before being served.

Question 46

What are the components in a waiting-line system?

Question 47

The ________ probability distribution is a continuous probability distribution often used to describe the service time in a queuing system.

Question 48

A(n) ________ queuing system has one line and one server.

Question 49

Describe the difference between FIFO and LIFO queue disciplines.

Question 50

Which of the following occurs as the level of service decreases?

A) Cost of waiting time decreases, and cost of providing service decreases.
B) Cost of waiting time decreases, and cost of providing service increases.
C) Cost of waiting time increases, and cost of providing service decreases.
D) Cost of waiting time increases, and cost of providing service increases.
E) Cost of waiting time first decreases, then increases; while cost of providing service decreases.

Question 51

Provide an example of a limited or finite population for a queue.

Question 52

What costs are present in waiting line analysis? How do these costs vary with the level of service?

Question 53

The study of waiting lines calculates the cost of providing good service but does not value the cost of customers' waiting time.

Question 54

Suppose that, on average, 4 customers arrive each minute in a Poisson distribution. P(x) is the probability of x arrivals. Which of the following is TRUE?

A) P(3) = P(4)
B) P(0) = 0
C) P(1) = 0.007
D) P(2) > P(5)
E) P(0) = P(1)

Question 55

Four of the most widely used waiting line models-M/M/1 or A, M/M/S or B, M/D/1 or C, and Finite population or D-all share three characteristics: Poisson arrivals, FIFO discipline, and exponential service times.

Question 56

A(n) ________ queuing system is one in which the customer receives service from only one station and then exits the system.

Question 57

A(n) ________ is a discrete probability distribution that often describes the arrival rate in queuing theory.

Question 58

The cost of waiting decreases as the service level increases.

Question 59

Of the three types of queue discipline, only ________ is assumed by the four primary waiting line models.

Question 60

Identify the seven major measures of a queue system's performance.

Question 61

A waiting line meeting the assumptions of M/M/1 has an average time between arrivals of 15 minutes, and it services items in an average of 10 minutes each. What is the utilization factor?

A) 0.25
B) 0.33
C) 0.50
D) 0.67
E) 1.50

Question 62

A queuing model that follows the M/M/1 assumptions has λ = 3 and μ = 2. What is the average number of units in the system?

A) -3
B) 3
C) 0.667
D) 150 percent
E) Growing without limit, since λ is larger than μ.

Question 63

Which of the following is NOT an assumption of the M/M/1 model?

A) The first customers to arrive are the first customers served.
B) Each arrival comes independently of the arrival immediately before and after that arrival.
C) The population from which the arrivals come is very large or infinite in size.
D) Customers do not renege.
E) Service times occur according to a normal probability distribution.

Question 64

A queuing model that follows the M/M/1 assumptions has λ = 10 and μ = 15. What is the average number of units in the system?

A) 0.83
B) 2
C) 2.5
D) 5
E) 6

Question 65

Which one of the following is NOT a characteristic of a Model C or M/D/1 system?

A) single server
B) single phase
C) Poisson arrival rate pattern
D) exponential service time pattern
E) unlimited population size

Question 66

An M/M/1 model and an M/D/1 model each have an arrival rate of 1 per minute and a service rate of 3 per minute; the average queue length of the M/D/1 will be twice that of the M/M/1.

Question 67

A waiting line model meeting the assumptions of M/M/1 has an arrival rate of 2 per hour and a service rate of 4 per hour. What is the utilization factor for the system?

A) 0.25
B) 0.33
C) 0.50
D) 0.67
E) 2.00

Question 68

A single-phase waiting-line system meets the assumptions of constant service time or M/D/1. Units arrive at this system every 12 minutes on average. Service takes a constant 8 minutes. What is the average length of the queue, L_q, in units?

A) 0.67
B) 2.5
C) 4.5
D) 5.0
E) 7.5

Question 69

Which one of the following is NOT a characteristic of a Model B or M/M/S system?

A) unlimited population size
B) single server
C) exponential service time pattern
D) single phase
E) Poisson arrival rate pattern

Question 70

In the M/M/1 waiting line model with an arrival rate of 3 per hour and a service rate of 6 per hour, the utilization factor for the system is approximately 0.333.

Question 71

Which one of the following is NOT a characteristic of a Model A or M/M/1 system?

A) exponential service time pattern
B) single number of servers
C) single number of phases
D) Poisson arrival rate pattern
E) finite population size

Question 72

A single-phase waiting-line system meets the assumptions of constant service time or M/D/1. Units arrive at this system every 10 minutes on average. Service takes a constant 6 minutes. What is the average length of the queue, L_q, in units?

A) 0.450
B) 0.133
C) 4.167
D) -2.083
E) 6

Question 73

A finite population waiting line model is also called M/M/1 with finite source.

Question 74

In the finite population waiting line model, the average length of the queue is calculated from the probability the system is empty.

Question 75

In the basic queuing model (M/M/1), what probability distribution describes arrival rates?

A) continuous
B) normal
C) negative exponential
D) Poisson
E) lognormal

Question 76

In the basic queuing model (M/M/1), what probability distribution describes service times?

A) binomial
B) negative exponential
C) Poisson
D) normal
E) lognormal

Question 77

Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. On average, how long does it take to service each student?

A) 1 minute
B) 2 minutes
C) 3 minutes
D) 5 minutes
E) 20 minutes

Question 78

The greater the margin by which the arrival rate exceeds the service rate, the better the performance of the waiting line.

Question 79

A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 5. What is the average number of units in the system?

A) 2/3
B) 1
C) 1.5
D) 2
E) 6

Question 80

A single-phase waiting-line system meets the assumptions of constant service time or M/D/1. Units arrive at this system every 10 minutes on average. Service takes a constant 8 minutes. What is the average number in the system, L_s, in units?

A) 1.60
B) 2.40
C) 0.80
D) 1.33
E) -3.13